Dual energy imaging in CT has been a promising technique since the first days of CT and was even mentioned in Godfrey Hounsfield's paper (1973) that introduced CT. The basic idea is to acquire two data sets at low and high energy levels and to use the pairs of the data sets to deduce additional information about the patient.
The physical basis of dual energy imaging includes two main mechanisms of the interaction of X rays with matter in the clinically relevant diagnostic energy-range from 30 keV to 140 keV, and the two interactions are photoelectric absorption and Compton scattering, each having its own functional dependence on x-ray energy. Photoelectric absorption is a rapidly decreasing function of energy while Compton scatter is a gentle function of energy. As shown in FIG. 1, the photoelectric interaction is a strong function of the atomic number of the absorbing tissue while scattering is nearly independent of Z. The physics enabled Alvarez and Macovski (1976) to develop a mathematical scheme, called dual-energy decomposition, to use the dual energy information.
In addition to the energy dependence, dual-energy decomposition must take X-ray sources into account. Since commercial clinical CT-scanners generally use polychromatic sources, the mathematics of dual energy imaging is not trivial. In this regard, single energy imaging with a polychromatic source does not have an exact and analytic solution. The current invention has the same above described physical bases but takes a somewhat different approach to the mathematics of dual-energy decomposition as will be described below. Assuming that:
Eenergy variableH, Llabels for high and low energy spectral or l (β, γ)integration path. This can be designated (in 2D CT) by aview and channel indices: β, γI(l)transmitted intensity along path lSH,L(E, γ)energy-weighted spectra where the channel index γ isincluded to account for the bow-tie filter.μ(E, x, y)the energy-dependent linear attenuation coefficient oftissues at voxel x, yμ1,2-H,Llinear attenuation coefficient for basis material 1 or 2averaged over the high (H)/low (L) spectra.μPE i (E),the photoelectric and Compton linear attenuationμC i (E)coefficients of tissue iμ1 (E), μ2 (E)the linear attenuation coefficients of known basis materials1 and 2gH L (l)projection datum with high or low spectra along path lc1 2 (x, y)how much the tissue at voxel x, y is like basis material1 or 2
Instead of the polynomial approximation method introduced by Alverez and Moscovski with its known drawbacks, an approach combining a linear term with a non-linear beam hardening term was proposed previously. Because the linear term is dominant, an iterative solution to the dual energy data domain decomposition converges rapidly and is stable. To derive, the transmitted intensity is given byI(l)=∫S(E,γ)exp[−∫lμ(E,x,y)dl]dE  (1)
The first key to dual energy CT is to realize that the attenuation coefficients are the sum of the physical processes. In the diagnostic energy range, the two dominant physical processes are photoelectric and Compton. Thus, the attenuation coefficient μ is expressed by the sum of μPE (photoelectric) and μC (Compton) as followsμ(E,x,y)=μPE(E,x,y)+μC(E,x,y)  (2)
Factorize the energy and spatial dependencies of the linear attenuation coefficient μ and a sum over the spatially dependent pairs of μPE and μC. Thus, Eqn. (2) is rewritten as:
                              μ          ⁡                      (                          E              ,              x              ,              y                        )                          =                              ∑            j                    ⁢                                          ⁢                                    δ                              i                ,                                  j                  ⁡                                      (                                          x                      ,                      y                                        )                                                                        ⁡                          (                                                                    μ                                          PE                      ,                      i                                                        ⁡                                      (                    E                    )                                                  +                                                      μ                                          C                      ,                      i                                                        ⁡                                      (                    E                    )                                                              )                                                          (        3        )            
where the sum goes over all tissue types labeled by i. The interpretation of Eqn. (3) is that at a given location x,y, the tissue is type
  j  ,            δ              i        ,        j              =                  {                                            1                                                                        if                  ⁢                                                                          ⁢                  i                                =                j                                                                        0                                                                        if                  ⁢                                                                          ⁢                  i                                ≠                j                                                    }            .      Replace the photoelectric and Compton by two known basis materials such as water and bone since one of which acts more like photoelectric (relatively high Z) and the other one acts more like Compton (relatively low Z):μ(E,x,y)≈μ1(E)c1(x,y)+μ2(E)c2(x,y)  (4)
where c1(x,y) and c2(x,y) respectively represent how much the voxel at x,y is like basis material 1 and 2. This substitution is a good approximation as long as:                the K-edge of any tissue of interest is not in the energy range where the two spectra SH,L are not small and        the two basis coefficients have different enough energy dependence in the energy range of interest.        
Even for a material whose K-edge is within this range such as iodine, the error may be small enough to be ignored.
It is very important that μ1 and μ2 have different energy dependencies. The energy dependence of photoelectric and Compton interactions is complicated functions of energy. But in the above specified diagnostic energy range, photoelectric goes approximately as E−3 while Compton is fairly flat (obeying the Klein-Nishida formula). High Z materials are dominated by photoelectric (depending on the energy, about Z4), while low Z materials are dominated by Compton as depicted in FIG. 1.
The linear attenuation coefficients for the basis coefficients are independent of location and are known. Next, Eqn. (4) is inserted into Eqn. (1). Since one equation has two unknowns, c1(x,y) and c2(x,y), two different spectra at high (H) and low (L) are needed to solve the two unknowns based upon the two equations. The result is:IH(l)=∫SH(E,γ)exp[−μ1(E)∫lc1(x,y)dl−μ2(E)∫lc2(x,y)dl]dE IL(l)=∫SL(E,γ)exp[−μ1(E)∫lc1(x,y)dl−μ2(E)∫lc2(x,y)dl]dE  (5)
Notice that the linear attenuation coefficients have been removed from the line path integrals. Now the projection data will be formed in the usual way by taking the logs:gH(l)=−ln∫SH(E,γ)exp[−μ1(E)L1(l)−μ2(E) L2(l)]dE gL(l)=−ln∫SL(E,γ)exp[−μ1(E)L2(l)−μ2(E) L2(l)]dE  (6)
where the following notation has been introduced:L1,2(l)=∫lc1,2(x,y)dl  (7)
The intermediate goal of the dual energy is to solve the two equations in (6) for L1,2 and then to reconstruct c1,2(x,y) by standard CT reconstruction techniques. The solution for L1,2 is discussed elsewhere including a pending patent application Ser. No. 12/106,907 filed on Apr. 21, 2008 and a reference entitled as “Analysis of Fast kV-switching in Dual Energy CT using a Pre-reconstruction Decomposition Technique,” by Yu Zou and Michael D. Silver (2009). These references are incorporated into the current application by external reference to supplement the specification. Thus, an iterative solution to the dual energy data domain decomposition converges rapidly and is stable because of a dominant linear term with a non-linear beam hardening term so as to derive the transmitted intensity.
Despite the above described dual-energy decomposition, the clinical significance of dual-energy imaging may still remain a matter of controversy. Among other x-ray means, no researcher has identified a single significant application of clinical importance that is unique to dual-energy CT. On the other hand, currently installed dual-energy CT systems have uncovered some areas of clinical significance in relation to the dual energy imaging technique. In spite of the lack of an indispensable killer application, the potentially significant clinical applications of the dual-energy CT include: 1) the improved images that are free of beam-hardening at a range of monochromatic energies with enhanced contrast among some tissue types; 2) the identification of the chemical composition in tissues, which may be also useful in explosive detection in scanned luggage, 3) more quantitative, accurate and precise data such as in detecting an early bio-marker for therapy progression assessment, analyzing bone mineral and assessing the fat content in liver for suitability for organ transplant; 4) automatic subtraction of a tissue type such as bone subtraction (predominately a photoelectric absorbing material) from soft tissue (predominately a scattering material), or iodine contrast from bone; and 5) attenuation correction in nuclear medicine.
Regardless of the clinical significance, several hurdles remain for successful dual energy imaging. Most importantly, for image quality, the temporal and spatial registrations must be sufficiently accurate for the high and low energy data sets. The image processing is performed on the high/low ray-sum pairs, and each pair should ideally represent the same path through the patient at the same time. Another important image quality issue is related to the different dose and noise levels between the two data sets. Depending on how the dual energy is achieved, the low energy data set could be very noisy compared with the high energy data set because x-ray tubes are less efficient at lower voltages and the lower energy X rays usually have worse penetration in tissues, which will be a problem for larger patients. Lastly, yet another significant hurdle is how to obtain the dual energy data sets in a cost effective manner.
In the past two years, prior art attempts have implemented certain dual energy CT systems. For example, Siemens has installed a number of dual source CT-scanners, which is equipped with two X-ray sources, and each runs at a different energy level for generating the two data sets. Another example is that Philips at their Haifa research facility has developed a sandwich detector where the upper layer records the low energy data and the lower layer records the high energy data. A prototype system is installed at the Hadassah Jerusalem Hospital. In this regard, GE has developed a specialized detector using garnet for capture 2496 total projections per rotation (TPPR) at a high speed. Another method is called slow kV-switching, which scans the same region of the patient twice. For example, for a circular scan, the first rotation is at high kV, and the tube voltage is then switched to low kV before or during the next rotation. In this regard, slow kV-switching is about a factor of 1000 to 2000 slower than fast kV-switching.
TABLE 1 below summarizes advantages and disadvantages of selected ways to acquire dual energy data sets. Fast kV-switching techniques change voltages between projections (also called views) so that the odd and even projections respectively correspond to the low or high tube voltage. Among these prior art approaches, the fast kV-switching appears an attractive technique for dual energy acquisition for a number of reasons. Since the dual source CT-scanners and the sandwich detector CT-scanners respectively require additional costs for the dual X-ray sources and the sandwich detectors, they may not be cost-effective to obtain dual energy data sets. Similarly, although GE's detector for fast kV-switching energy CT is not summarized in TABLE 1, the semi-precious gem detector also incurs additional costs. In addition, both the dual source CT-scanners and the sandwich detector CT-scanners must resolve other technical difficulties that are associated with these systems as listed in the table below. On the other hand, although the slow kV-switching does not require additional parts or equipment, dual energy data sets result in poor temporal registration that is off by at least one rotation period as well as poor spatial registration in particular from helical scans. For these reasons, the prior art technologies remain to find a cost effective system and method to utilized the dual energy data for CT.
TABLE 1OptionsAdvantagesDisadvantagesFast kV-switchingTemporal and spatialLimited energy separation(alternating views)registration very good.unless square-wave waveformData domain methodsdeveloped.possible leading to better IQDifficult to equalize dose/noiseand flexibility.between high/low data sets.Helical acquisition noDevelopment time and cost forproblem.fast, switching HVPS.Slow kV-switchingGood energy separation.Poor temporal registration; off(alternating rotations)Easy to equalize dose/noiseby at least one rotation period.between high/low data sets.Poor spatial registration,Little equipmentespecially if doing helical scansdevelopment necessary.and thus limited to imageLittle or no added H/Wdomain methods.costs.Helical scans may require lowerpitch and thus more dose.Dual sourceGood energy separation.Temporal registration off by ¼Easy to equalize dose/noiseof the rotation period.between high/low data sets.Spatial registration requires tubealignment.Cost of two imaging chains.Field-of-view for dual energylimited by the smaller of the twoimaging chains.Cross-scatter contamination.Sandwich detectorPerfect temporal and spatialLimited energy separation.registration.Cost and development of theData domain decompositiondetector.methods valid.Helical acquisition noproblem.
As illustrated in FIG. 2A, the fast kV-switching technique alternately changes voltages between projections (also called views) so that the odd and even projections correspond to either the low or high tube voltage as the X-ray tube moves in a direction as indicated by an arrow Although the switching X-ray ideally should have square waveforms, the X-ray may be closer to a sinusoidal waveform in reality as illustrated in FIG. 2B. In the current invention, square-wave and sinusoidal waveforms have been compared for fast kV-switching in resultant image quality and the dual energy decomposition. Please note that square-wave is the same as slow kV-switching if we ignore registration problems.
As already shown in TABLE 1, prior art fast kV-switching techniques without the use of dual sources or special detectors nonetheless have both advantages and disadvantages in acquiring dual energy data sets. The prior art fast kV-switching techniques have very good temporal and spatial registrations between corresponding high and low energy projections, which make data domain methods possible and lead to better IQ and flexibility. In addition, prior art fast kV-switching techniques acquire good dual energy data sets also through helical projections.
A disadvantage is the one view misregistration between corresponding high and low energy projections. Another problem is the difficulty of high noise in the low energy data because it may be technically difficult to swing the mA as fast as the kV. The current invention addresses these issues through a series of numerical simulation studies for improvement without necessarily involving the prior art solutions such as dual energy sources, specialized detectors or slow switching. A preferred embodiment will be described for fast kV-switching, spectra generation, and polychromatic data generation.
With respect to the current application, dual energy decomposition takes place in the data domain (before reconstruction) because of its greater flexibility compared with image domain (after reconstruction) decomposition. Therefore, the current invention will assume a data domain decomposition approach.